Properties

Label 3234.2.bw
Level 3234
Weight 2
Character orbit bw
Rep. character \(\chi_{3234}(89,\cdot)\)
Character field \(\Q(\zeta_{42})\)
Dimension 2256
Sturm bound 1344

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.bw (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 8160 2256 5904
Cusp forms 7968 2256 5712
Eisenstein series 192 0 192

Trace form

\( 2256q - 188q^{4} - 28q^{6} - 16q^{7} - 32q^{9} + O(q^{10}) \) \( 2256q - 188q^{4} - 28q^{6} - 16q^{7} - 32q^{9} + 24q^{15} + 188q^{16} + 24q^{19} - 16q^{21} + 12q^{24} + 196q^{25} - 8q^{28} - 8q^{30} - 24q^{31} + 20q^{36} + 68q^{37} + 12q^{39} + 48q^{42} - 16q^{43} - 48q^{45} + 312q^{46} + 40q^{49} + 12q^{51} - 32q^{52} + 36q^{54} + 60q^{57} + 52q^{58} + 12q^{60} - 112q^{61} + 56q^{63} + 376q^{64} + 8q^{67} - 32q^{70} - 48q^{73} - 132q^{75} + 32q^{81} - 24q^{82} - 80q^{84} - 128q^{85} + 36q^{87} - 84q^{90} + 16q^{91} + 536q^{93} + 48q^{94} + 12q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database